In many practical real-time applications, there is a given set of task frequencies (i.e., inverse of task periods) corresponding to predetermined QoS options that the applications can choose. For example, in audio applications, the typical choices of playback frequencies are for CD quality, radio quality, and phone quality. Similar configurations can be found in streaming video and in control applications. In such systems, applications dynamically arrive requesting one of the periods provided by the QoS manager. Thus, the accurate and efficient online schedulability test is essential for any task set whose periods are chosen from the QoS period set. For this purpose, we propose new utilization bounds as a function of given QoS periods. As long as there is a set of given periods that can be chosen by applications, the bounds developed can be used by the QoS manager to quickly determine the schedulability of dynamic applications.